In biochemistry

Biochemistry

Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

, the MWC model (also known as the concerted model or symmetry model) describes allosteric transitions of proteins made up of identical subunits. It was proposed by Jean-Pierre Changeux

Jean-Pierre Changeux

Jean-Pierre Changeux is a French neuroscientist known for his research in several fields of biology, from the structure and function of proteins , to the early development of the nervous system up to cognitive functions...

 based on his PhD experiments, and described by Jacques Monod

Jacques Monod

Jacques Lucien Monod was a French biologist who was awarded a Nobel Prize in Physiology or Medicine in 1965, sharing it with François Jacob and Andre Lwoff "for their discoveries concerning genetic control of enzyme and virus synthesis"...

, Jeffries Wyman, and Jean-Pierre Changeux

Jean-Pierre Changeux

Jean-Pierre Changeux is a French neuroscientist known for his research in several fields of biology, from the structure and function of proteins , to the early development of the nervous system up to cognitive functions...

. It stands in opposition to the sequential model

Sequential model

The sequential model is a theory that describes co-operativity of protein subunits.-Overview:This model suggests that the subunits of multimeric proteins have two conformational states. The binding of the ligand causes conformational change...

.

The main idea of the model is that regulated protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s, such as many enzyme

Enzyme

Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

s and receptor

Receptor (biochemistry)

In biochemistry, a receptor is a molecule found on the surface of a cell, which receives specific chemical signals from neighbouring cells or the wider environment within an organism...

s, exist in different interconvertible states in the absence of any regulator. The ratio of the different conformational states is determined by thermal equilibrium

Chemical equilibrium

In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

. The regulators merely shift the equilibrium toward one state or another. For instance, an agonist

Agonist

An agonist is a chemical that binds to a receptor of a cell and triggers a response by that cell. Agonists often mimic the action of a naturally occurring substance...

 will stabilize the active form of a pharmacological receptor

Receptor (biochemistry)

In biochemistry, a receptor is a molecule found on the surface of a cell, which receives specific chemical signals from neighbouring cells or the wider environment within an organism...

. Phenomenologically, it looks as if the agonist provokes the conformational transition. One crucial feature of the model is the dissociation between the binding function (the fraction of protein bound to the regulator), and the state function (the fraction of protein under the activated state), cf below. In the models said of "induced-fit", those functions are identical.

In the historical model, each allosteric unit, called a protomer

Protomer

In structural biology, a protomer is the structural unit of an oligomeric protein. A protomer can be a protein subunit or several different subunits, that assemble in a defined stoichiometry to form an oligomer. The protomer is the smallest subset of different subunits that form the oligomer. The...

 (generally assumed to be a subunit), can exist in two different conformational states - designated 'R' (for relaxed) or 'T' (for tense) states. In any one molecule, all protomers must be in the same state. That is to say, all subunits must be in either the R or the T state. Proteins with subunits in different states are not allowed by this model. The R state has a higher affinity for the ligand than the T state. Because of that, although the ligand may bind to the subunit when it is in either state, the binding of a ligand will increase the equilibrium in favor of the R state.

Two equations can be derived, that express the fractional occupancy of the ligand binding site (Y) and the fraction of the proteins in the R state (R):





Where is the allosteric constant, that is the ratio of proteins in the T and R states in the absence of ligand, is the ratio of the affinities of R and T states for the ligand, and , the normalised concentration of ligand.

This model explains sigmoidal

Sigmoid function

Many natural processes, including those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used. A sigmoid curve is produced by a mathematical...

 binding properties as change in concentration of ligand over a small range will lead to a vast increase in the proportion of molecules in the R state, and thus will lead to a high association of the ligand to the protein.

The MWC model proved very popular in enzymology, and pharmacology

Pharmacology

Pharmacology is the branch of medicine and biology concerned with the study of drug action. More specifically, it is the study of the interactions that occur between a living organism and chemicals that affect normal or abnormal biochemical function...

, although it has been shown inappropriate in a certain number of cases. The best example of a successful application of the model is the regulation of hemoglobin

Hemoglobin

Hemoglobin is the iron-containing oxygen-transport metalloprotein in the red blood cells of all vertebrates, with the exception of the fish family Channichthyidae, as well as the tissues of some invertebrates...

function. Extension of the model have been proposed for lattices of proteins, for instance by Changeux, Thiery, Tung and Kittel, by Wyman or by Duke, Le Novere and Bray.